mlsanityData to 7 Oct 2026

Counterfactual Explanations for Arbitrary Regression Models

arXiv 2106.15212 ↗First posted 29 Jun 2021cs.LG cs.AI cs.CCcited by 22

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Abstract (arXiv)

We present a new method for counterfactual explanations (CFEs) based on Bayesian optimisation that applies to both classification and regression models. Our method is a globally convergent search algorithm with support for arbitrary regression models and constraints like feature sparsity and actionable recourse, and furthermore can answer multiple counterfactual questions in parallel while learning from previous queries. We formulate CFE search for regression models in a rigorous mathematical framework using differentiable potentials, which resolves robustness issues in threshold-based objectives. We prove that in this framework, (a) verifying the existence of counterfactuals is NP-complete; and (b) that finding instances using such potentials is CLS-complete. We describe a unified algorithm for CFEs using a specialised acquisition function that composes both expected improvement and an exponential-polynomial (EP) family with desirable properties. Our evaluation on real-world benchmark domains demonstrate high sample-efficiency and precision.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). Builds on 27 of its 68 references that are in the map. First posted on arXiv 29 Jun 2021.

Builds on

27 of 68 references.

References · 27

  1. 2016Categorical Reparameterization with Gumbel-Softmaxcited by 2,708
  2. 2017Explanation in Artificial Intelligence: Insights from the Social Sciencescited by 1,201
  3. 2016The Concrete Distribution: A Continuous Relaxation of Discrete Random Variablescited by 1,135
  4. 2017Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPRcited by 1,086
  5. 2019Explaining Machine Learning Classifiers through Diverse Counterfactual Explanationscited by 612
  6. 2018Actionable Recourse in Linear Classificationcited by 327
  7. 2020Algorithmic Recourse: from Counterfactual Explanations to Interventionscited by 250
  8. 2019FACE: Feasible and Actionable Counterfactual Explanationscited by 232
  9. 2019Interpretable Counterfactual Explanations Guided by Prototypescited by 223
  10. 2020Multi-Objective Counterfactual Explanationscited by 157
  11. 2019Learning Model-Agnostic Counterfactual Explanations for Tabular Datacited by 146
  12. 2019Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifierscited by 143
15 more
  1. 2017Non-convex Optimization for Machine Learningcited by 132
  2. 2019The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasonscited by 115
  3. 2018The Blessings of Multiple Causescited by 103
  4. 2017Interpretable Predictions of Tree-based Ensembles via Actionable Feature Tweakingcited by 76
  5. 2020On Counterfactual Explanations under Predictive Multiplicitycited by 73
  6. 2019Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variablescited by 64
  7. 2019Bayesian Optimisation over Multiple Continuous and Categorical Inputscited by 55
  8. 2019Bayesian Optimization of Composite Functionscited by 45
  9. 2020Decisions, Counterfactual Explanations and Strategic Behaviorcited by 44
  10. 2019FOCUS: Flexible Optimizable Counterfactual Explanations for Tree Ensemblescited by 43
  11. 2019On the computation of counterfactual explanations -- A surveycited by 33
  12. 2020Convex Density Constraints for Computing Plausible Counterfactual Explanationscited by 32
  13. 2019Mixed-Variable Bayesian Optimizationcited by 29
  14. 2020The Complexity of Gradient Descent: CLS = PPAD cap PLScited by 17
  15. 2018Fair lending needs explainable models for responsible recommendationcited by 12

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 5; 2023: 5; 2024: 4; 2025: 3; 2026: 2.

22 papers.

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  1. 2022Robust Counterfactual Explanations for Tree-Based Ensemblescited by 49
  2. 2022Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recoursecited by 40
  3. 2022On the Privacy Risks of Algorithmic Recoursecited by 32
  4. 2021Toward Explainable AI for Regression Modelscited by 30
  5. 2021ReLAX: Reinforcement Learning Agent eXplainer for Arbitrary Predictive Modelscited by 25
  6. 2021Counterfactual Shapley Additive Explanationscited by 22
  7. 2022On the Trade-Off between Actionable Explanations and the Right to be Forgottencited by 20
  8. 2024Counterfactual Metarules for Local and Global Recoursecited by 7
  9. 2025Mitigating Clever Hans Strategies in Image Classifiers through Generating Counterexamplescited by 6
  10. 2023Faithful Model Explanations through Energy-Constrained Conformal Counterfactualscited by 5
  11. 2025Diffusion Counterfactuals for Image Regressorscited by 5
  12. 2024Counterfactual Explanations for Deep Learning-Based Traffic Forecastingcited by 3
10 more
  1. 2023Counterfactual Explanations of Neural Network-Generated Response Curvescited by 2
  2. 2023Unveiling the Potential of Counterfactuals Explanations in Employabilitycited by 2
  3. 2023Counterfactual Explanation for Regression via Disentanglement in Latent Spacecited by 1
  4. 2022Decomposing Counterfactual Explanations for Consequential Decision Makingcited by 0
  5. 2023On the Connection between Game-Theoretic Feature Attributions and Counterfactual Explanationscited by 0
  6. 2024No Dtrain: Model-Agnostic Counterfactual Explanations Using Reinforcement Learningcited by 0
  7. 2024Relevance-aware Algorithmic Recoursecited by 0
  8. 2025ACE: Adapting sampling for Counterfactual Explanationscited by 0
  9. 2026Counterfactual Training: Teaching Models Plausible and Actionable Explanationscited by 0
  10. 2026CEL: Comprehensive Counterfactual Explanations Library and Benchmarkcited by 0